The importance of rate-dependent effects in modelling the micro-damage process zone in cortical bone fracture

Abstract

A greater mechanistic understanding of bone’s fracture process is important to the development of better diagnostic and therapeutics for bone fragility and fracture. To aid in better understanding the fracture process of bone, in earlier work, a continuum damage mechanics (CDM)-based computational model was developed and experimentally validated for modelling the micro-damage process zone (MDPZ). The MDPZ is an important intrinsic toughening mechanism that forms during cortical bone fracture. Interestingly, to accurately model the MDPZ in the CDM-based model, rate-dependent effects were required. This was achieved by using a viscosity regularization scheme available in ABAQUS, the commercial FE software used to develop the model. In this study, a review of the CDM-based model is given, after which it is used to explore the significance of rate-dependent effects on the formation of the MDPZ. Specifically, we show how variations in the rate-dependent effect drastically affects the formation of the MDPZ. Furthermore, using data from previous work carried out by Willett and co-workers, irradiated bovine cortical bone was used as a case study to demonstrate the need for accounting for rate dependent effects in modelling the MPDZ. In this paper, it is shown that even if other degraded mechanical properties are accounted for, there is still a need to account for the reduction in rate-dependent effects, because of the irradiation, to accurately model the MDPZ and match experimental load deflection curves and J-integral fracture toughness values.The importance of rate dependency in MPDZ formation alludes to a strain rate hardening mechanism at play in its formation which has been previously explored in other biological nanocomposites such as nacre. In addition, it adds credence to the importance of the organic phase and probably the importance of intra- and interfibrillar interfaces found in the mineralised collagen fibril to bone’s intrinsic fracture resistance.